132 LearnersLast updated on May 26th, 2025
Square Root of 550
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 550.
What is the Square Root of 550?
The square root is the inverse of the square of a number. 550 is not a perfect square. The square root of 550 is expressed in both radical and exponential form. In radical form, it is expressed as √550, whereas (550)(1/2) is the exponential form. √550 ≈ 23.452, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 550
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like long-division and approximation are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 550 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 550 is broken down into its prime factors:
Step 1: Finding the prime factors of 550 Breaking it down, we get 2 x 5 x 5 x 11: 21 x 52 x 111
Step 2: Now we found the prime factors of 550. The second step is to make pairs of those prime factors. Since 550 is not a perfect square, the digits of the number can’t be grouped in a complete pair.
Therefore, calculating 550 using prime factorization alone is incomplete.
Square Root of 550 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 550, we need to group it as 50 and 5.
Step 2: Now we need to find n whose square is ≤ 5. We can say n is ‘2’ because 2 x 2 = 4, which is less than or equal to 5. Now the quotient is 2, after subtracting 4 from 5, the remainder is 1.
Step 3: Bring down 50, which is the new dividend. Add the old divisor with the same number 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor is 4n. Now we need to find the value of n such that 4n x n ≤ 150. Let us consider n as 3, now 43 x 3 = 129.
Step 5: Subtract 129 from 150, the difference is 21, and the quotient is 23.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2100.
Step 7: Now we need to find the new divisor, which is 466 because 466 x 4 = 1864.
Step 8: Subtracting 1864 from 2100, we get 236.
Step 9: Continue these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.
So the square root of √550 is approximately 23.45.
Square Root of 550 by Approximation Method
The approximation method is another easy method to find the square roots. Now let us learn how to find the square root of 550 using the approximation method.
Step 1: Identify the closest perfect squares to 550. The smallest perfect square less than 550 is 529, and the largest perfect square greater than 550 is 576. √550 falls somewhere between 23 and 24.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula, (550 - 529) ÷ (576 - 529) = 21/47 ≈ 0.447 Using the formula, we identified the decimal point of our square root.
The next step is adding the value we got initially to the decimal number, which is 23 + 0.447 ≈ 23.447, so the square root of 550 is approximately 23.447.
Common Mistakes and How to Avoid Them in the Square Root of 550
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually focus on the positive square root, as it is often the desired solution in real-world applications. For example: √50 ≈ 7.071, but there is also -7.071.
Square Root of 550 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √550?
The area of the square is approximately 550 square units.
Explanation
The area of the square = side².
The side length is given as √550.
Area of the square = (√550)² = 550.
Therefore, the area of the square box is approximately 550 square units.
Problem 2
A square-shaped building measuring 550 square meters is built; if each of the sides is √550, what will be the square meters of half of the building?
275 square meters
Explanation
We divide the given area by 2 as the building is square-shaped.
Dividing 550 by 2 = 275
So half of the building measures 275 square meters.
Problem 3
Calculate √550 x 5.
Approximately 117.26
Explanation
The first step is to find the square root of 550, which is approximately 23.45.
The second step is to multiply 23.45 by 5. So 23.45 x 5 ≈ 117.26.
Problem 4
What will be the square root of (550 + 50)?
The square root is approximately 24.
Explanation
To find the square root, we need to find the sum of (550 + 50). 550 + 50 = 600, and then √600 ≈ 24.49.
Therefore, the square root of (550 + 50) is approximately ±24.49.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √550 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 86.9 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√550 + 20) = 2 × (23.45 + 20) = 2 × 43.45 ≈ 86.9 units.
FAQ on Square Root of 550
1.What is √550 in its simplest form?
2.Mention the factors of 550.
3.Calculate the square of 550.
4.Is 550 a prime number?
5.550 is divisible by?
Important Glossaries for the Square Root of 550
- Square root: A square root is the inverse of a square. Example: 42 = 16, and the inverse square is the square root, so √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root is more commonly used in real-world applications. It is also known as the principal square root.
- Perfect square: A perfect square is an integer that is the square of another integer. For example, 144 is a perfect square because it is 122.
- Long division method: A method used to find the square root of non-perfect square numbers through a series of division steps.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
